 
Summary: 1. Interpretations.
1.1. Review of terms and statements.
Remark 1.1. Suppose t is a term. Then exactly one of the following hold:
(T1) t = x for some x X;
(T2) t = c for some c C;
(T3) t = f(t1, . . . , tn) for some n N+
, some f Fn and some terms t1, . . . , tn.
Suppose A is a statement. Then exactly one of the following hold:
(S1) A = r(t1, . . . , tn) for some n N+
, some r Rn and some terms t1, . . . , tn;
(S2) A = x B for some x X and some statement B;
(S3) A = x B for some x X and some statement B;
(S4) A = ( s = t ) for some terms s, t;
(S5) A = B for some statement B;
(S6) A = ( B b C ) for some statements B, C and some b {, , , }.
1.2. Interpretations.
Definition 1.1. An interpretation of a first order language is an ordered quadru
ple
I = (D, C, F, R)
such that D is a set and C, F, R are functions with domains C, F, R, respec
